As far as i'm aware, its ok to use the same computer provided you all deposit via different cards (details will be checked). My girlfriend and I both used to play on
party poker on the same comp. Obviously you cant enter the same tourneys though. I got in trouble for registering both our names for a freeroll so that if I went out early, she could carry on using her's. That was a bit cheeky, but apart from that, as long as you run them as 3 seperate accounts you'll be ok.
Should you come to want to withdraw somewhere down the line, they may ask for additional I.D. to prove your not multi-accounting, and check you've not been chip dumping each other etc.
I logged on to one of my sites at a friends house who plays on the same site recently, it just asked a few security Q's before I was allowed access to my account (making sure I wasn't a multi-accounter).
Be aware though, there are still sites that only allow one account per household, though I can only think of one at present. Most sites relaxed that rule when poker really took off as a hobby for anyone.